Inverse systems of abstract Lebesgue spaces
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- by Bruce Christianson PDF
- Proc. Amer. Math. Soc. 110 (1990), 855-857 Request permission
Abstract:
We show that inverse limits exist in the category of ${L^1}$ spaces and positive linear contractions between them. This result generalizes the wellknown classical results for inverse systems of Choquet Simplexes and of $L$-balls, but our proof is simple and more purely geometrical. The result finds physical application in the study of random fields.References
- E. B. Davies and G. F. Vincent-Smith, Tensor products, infinite products, and projective limits of Choquet simplexes, Math. Scand. 22 (1968), 145–164 (1969). MR 243316, DOI 10.7146/math.scand.a-10879
- D. A. Edwards, On the homeomorphic affine embedding of a locally compact cone into a Banach dual space endowed with the vague topology, Proc. London Math. Soc. (3) 14 (1964), 399–414. MR 169019, DOI 10.1112/plms/s3-14.3.399
- David A. Edwards, Systèmes projectifs d’ensembles convexes compacts, Bull. Soc. Math. France 103 (1975), no. 2, 225–240. MR 397359
- Francis Jellett, Homomorphisms and inverse limits of Choquet simplexes, Math. Z. 103 (1968), 219–226. MR 221278, DOI 10.1007/BF01111040
- A. J. Lazar, The unit ball in conjugate $L_{1}$ spaces, Duke Math. J. 39 (1972), 1–8. MR 303242
- Lucien Le Cam, Asymptotic methods in statistical decision theory, Springer Series in Statistics, Springer-Verlag, New York, 1986. MR 856411, DOI 10.1007/978-1-4612-4946-7
- Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
- Gerhard Winkler, Choquet order and simplices with applications in probabilistic models, Lecture Notes in Mathematics, vol. 1145, Springer-Verlag, Berlin, 1985. MR 808401, DOI 10.1007/BFb0075051
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 855-857
- MSC: Primary 46M10; Secondary 46B25
- DOI: https://doi.org/10.1090/S0002-9939-1990-1030734-3
- MathSciNet review: 1030734